Problem Set 6 ECN 134 Financial Economics Prof Farshid Mojaver On Financial Crisis 1 What was the role of deregulation in the financial crisis of 2008 2 What is systemic risk How did it happen during the financial crisis of 2008 3 Why housing prices increased so dramatically from 2001 to 2004 Risk and Return 1 You consider investing in one of three portfolios X Y or Z for one year The following matrix gives the means and standard deviations of annual returns in for the three portfolios annual returns are distributed normally X Y Z Mean 5 7 5 Std Dev 20 20 10 Rank the three portfolios in order of the probability of i the one year return being negative ii the one year return being less than 5 iii the one year return being less than 10 Hint you do not need a table for the normal distribution to arrive at the correct answers to i through iii iv Could you imagine a rational investor preferring X to Y v Could you imagine a rational investor preferring X to Z vi Could you imagine a risk averse investor preferring X to Z 2 Based on the scenarios below what is the expected return for a portfolio with the following return profile Market Condition Bear Probability Normal 0 2 0 3 Bull 0 5 Rate of return 25 10 24 Use the following scenario analysis for Stocks X and Y to answer Problems 3 through 5 round to the nearest percent Normal Bear Market Bull Market Market Probability 0 2 0 5 0 3 Stock X 20 Stock Y 15 3 What are the expected rates of return for Stocks X and Y 18 50 20 10 4 What are the standard deviations of returns on Stocks X and Y 5 Assume that of your 10 000 portfolio you invest 9 000 in Stock X and 1 000 in Stock Y What is the expected return on your portfolio Part A Optimal Risky Portfolio 1 Stocks offer an expected rate of return of 18 with a SD of 22 Gold offers an expected return of 10 with a SD of 30 a In light of the apparent inefficiency of gold with respect to both mean return and volatility would anyone hold gold If so demonstrate graphically why one would do so b Given the data above reanswer a with the additional assumption that the correlation coefficient between gold and stock equals 1 Draw a graph illustrating why one would or would not hold gold in one s portfolio Could this set of assumptions for expected return SD and correlation represent equilibrium for the security market 2 Suppose you have a project that has 70 chance of doubling your investment in a year and 30 chance of halving your investment in a year What is the standard deviation of the rate of return on this investment 3 Suppose that you have 1 million and the following two opportunities from which to construct a portfolio a Risk free asset earning 12 per year b Risky asset with expected return 30 per year and standard deviation of 40 If you construct a portfolio with a standard deviation of 30 what is the expected rate of return 4 Statistics fro three stocks A B and C are shown in the following tables Standard Deviations of Returns Stock A B C Standard Deviation 40 20 40 Correlations of Returns Stock A B C A 1 00 0 90 0 50 1 00 0 10 B C 1 00 Based only on the information provided in the tables and given a choice between a portfolio made up of equal amounts of stocks A and B or a portfolio made up of equal amounts of stocks B and C state which portfolio you would recommend Justify your choice 5 Input the data from the table into a spreadsheet Compute the serial correlation in decade returns for each asset class and for inflation Also find the correlation between the returns of various asset classes What do he data indicate 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s Small company Stocks 3 72 7 28 20 63 19 01 13 72 8 75 12 46 13 84 Large company Stocks 18 36 1 25 9 11 19 41 7 84 5 90 17 60 18 20 Long term Government 3 98 4 60 3 59 0 25 1 14 6 63 11 50 8 60 Intermediate term Govt 3 77 3 91 1 70 1 11 3 41 6 11 12 01 7 74 Treasury bills 3 56 0 30 0 37 1 87 3 89 6 29 9 00 5 02 Inflation 1 00 2 04 5 36 2 22 2 52 7 36 5 10 2 93 6 An investor s portfolio consists of two assets one MSFT producing computer software and the other GOOG selling internet advertising Ten years of hypothetical data on returns in percent for these two stocks are given below save these data for use next week also Date 1998 1999 2000 2001 2002 MSFT 4 64 10 80 8 88 10 32 9 36 GOOG 5 98 12 74 9 10 9 88 6 11 Date 2003 2004 2005 2006 2007 MSFT 10 80 6 88 13 76 13 76 7 44 GOOG 14 56 11 57 4 03 16 51 11 18 a Based on these data what is the expected return on MSFT GOOG b What is the variance of return for MSFT The standard deviation Do the same calculation for GOOG Be sure to use one less than the number of observations as the denominator in the variance formula c What is the covariance of MSFT returns with GOOG returns What is the correlation of the two returns Write out the formulas you use explicitly 7 Non CAMP Portfolio Return and Risk Two Assets a What is the return and risk of a portfolio with no MSFT stock and all GOOG stock No GOOG stock and all MSFT stock Use S D not the variance to characterize risk b Evaluate the return and risk for each of the weight combinations below MSFT 0 2 5 6 7 1 GOOG 1 8 5 4 3 0 Carry four digits Table your results with the two columns of weights next to the column of portfolio expected returns next to the portfolio standard deviation risk c Plot the expected returns and risk tabled above Use some graph paper or measure and draw lines very carefully or use a spreadsheet Fill in the gaps between the weights I had you calculate with your best guess d On both the table and the graph identify both the feasible set and the efficient set Do they differ Why or why not Assume that no risk free asset is available e What proportion of MSFT would you hold Why Do we know what another investor would hold Why or why not f Is it possible for the feasible set to be backward bending when the correlation between the returns of assets i and j is positive i e when 0 or is it necessary …